I could be misunderstanding what Broadcast does, but I thought it meant to not advertise the SSID for that wireless AP.

So for my 2.4GHz network, I unchecked Broadcast, put in an SSID and disabled security.
The router is set to ignore DHCP requests from unknown devices so no one can connect till I map their MAC address to an IP anyways.

But in both Windows and Linux PCs, I can see the SSID in the list of available networks.

Is un-checking broadcast the way to make a hidden network and this could be a bug?
Or is there another way to make a hidden wireless network?

Non-broadcasting just breaks standards, and encourages your neighbour to install their new wifi on same channel. The SSID is still visible in some circumstances (to sniffers), so no real security (by obscurity?). Once you have told the client what to look for maybe it remembers the name? Some clients show you there's something there but require the name to connect, others don't show.

I just have a couple different handheld devices that either have trouble connecting (or won't at all) to wireless APs that have any kind of encryption.
So I have to have a wireless network without encryption.

Having it not broadcast was just to discourage neighbours from trying to connect, and seeing as I am in a rural place with the only wireless router running, conflicting channels and whatnot shouldn't be a big problem. But the router ignores requests from unknown devices and everything has a static IP (they couldn't get on anyways if they knew the SSID).